LHCb strategies for γ from B → DK 7 0 Y. Xie a (on behalf of the LHCb Collaboration) 0 2 aSchool of Physics, University of Edinburgh, Mayfield Road, Edinburgh EH9 3JZ, UK n a OneofthemostpromisingwaystodeterminetheangleγoftheCKMunitaritytriangleisthroughmeasurement J ofthetreelevelprocessesB→DK. TheLHCbcollaboration hasstudiedthepotentialofthesedecaysemploying 5 the Atwood-Dunietz-Soni (ADS) and Dalitz methods, making use of a large sample of simulated data. For each 1 method theexpected sensitivities to the angle γ are presented in thisreport. 1 v 8 1. INTRODUCTION tobeimprovedtoatleast5o [1]tomatchthepre- 2 0 cision of its indirect estimate from a global fit to Thisreportisarrangedasfollows. InSection1 1 CKM parameters excluding direct measurements 0 we present a physics motivation, followed by a of γ. 7 general discussion of B → DK decays 1. Sec- In LHCb, the tree level decays B0 → D±K∓ 0 tion2givesabriefdescriptionoftheLHCbdetec- s s can also be used to determine the angle γ in a / x tor, the simulation and the event selection tech- theoretically clean way. This measurement is ex- e niques. An introduction to the ADS method to pected to have a sensitivity of 14o with 2 fb−1 of - extract the CKM angle γ from B → DK decays p data. WewillseebelowthattheB →DK decays e and its application and expected performance in have a greater statistical sensitivity to the angle h LHCb is presented in Section 3. Section 4 de- γ with an equivalent amount of data. : v scribes the use of the Dalitz method to extract γ i from B → DK decays and the expected LHCb X sensitivities. We conclude in Section 5. r a 1.1. Motivation In B hadron decays, tree level processes are 1.2. Features of B →DK decays generally dominated by Standard Model contri- The CKM favoured process B → D¯0K and butions while new physics mainly affects loop di- disfavoured process B → D0K can be described agrams. Any difference between the CKM uni- with three parameters: a weak phase difference taritytriangleasmeasuredintreelevelprocesses γ ≡ arg(−(V V∗/(V V∗)), a strong phase dif- compared to loop level processes would indicate ud ub cd cb ference δ and the ratio of magnitudes between new physics in the flavour sector. Currently the B the disfavouredandfavouredamplitudes, defined unitarity triangle as determined by the tree level as r . If the D¯0 and D0 decay to a common fi- measurementsofγ andthe CKMmatrixelement B nal state, then the interference between the two |V | is consistent with the triangle determined ub amplitudes via D¯0 and D0 allows the extraction by measurements of the loop dominated parame- the angle γ with several methods, as illustrated ters ǫ , ∆m , ∆m and sin2β [1]. However, the k d s below. present measurements of γ from B → DK at B It is expected that r is small in the B± → factories have large errors: γ = (92±41±11± B 12)o(BaBar) [2], γ =(53+15±3±9)o(Belle) [3]. DK± case and has a value of about 0.1 [4,5] due −18 to colour suppression in the CKM disfavoured TheprecisionontheangleγfromB →DK has amplitude. For B¯0 → DK¯∗0, both amplitudes 1In this report D represents a D0 or D¯0, B represents a arecoloursuppressed,thereforerB isexpectedto B±,B0 orB¯0 andK representsaK±,K∗0 orK¯∗0. be larger [5]. 1 2 2. THE LHCb DETECTOR struction of non-CP eigenstates for decays com- mon to both D0 and D¯0. An example is the The LHCb detector is a single arm spectrom- hadronic final state Kπ, which may arise from eter dedicated to the study of CP violation in the Cabibbo favoured (CF) decay D¯0 → K+π− B meson decays at the Large Hadron Collider, or the doubly-Cabibbo suppressed (DCS) decay which will start operation at CERN in 2007. D0 → K+π−. The relation between the CF and The detector andits expected performanceis de- the DCS decayis describedby a magnitude ratio scribed in detail in [6]. Here we only empha- rKπ and a strong phase difference δKπ: size that LHCb has a 94% tracking efficiency for D D tracks with momentum above 10 GeV/c, a 93% A(D¯0 →K−π+) A(D0 →K+π−) K± identification efficiency and a corresponding rDKπeiδDKπ ≡ A(D0 →K−π+) = A(D¯0 →K+π−).(1) probabiltyof4.7%foraπ± tobe misidentifiedas a K± for the momentum range 2−100 GeV/c. Therefore there are four possible B decays, whose decay rates can be written as follows 2.1. Data simulation and event selection Monte Carlo simulation data produced with Γ(B− →(K−π+)DK−)∝ Pythia and Geant4 are used to study the trig- 1+(r rKπ)2+2r rKπcos(δ −δKπ −γ), (2) ger,thereconstructionandeventselection,which B D B D B D in turn allows the physics performance to be as- Γ(B− →(K+π−)DK−)∝ sessed. r2 +(rKπ)2+2r rKπcos(δ +δKπ−γ), (3) We use event samples consisting of 260 mil- B D B D B D lion minimum bias event for trigger studies, 140 Γ(B+ →(K+π−)DK+)∝ million inclusive b¯b events and dedicated signal 1+(r rKπ)2+2r rKπcos(δ −δKπ +γ), (4) B D B D B D events for selection and background studies. Sensitivities on physics parameters are ob- Γ(B+ →(K−π+)DK+)∝ tained using fast simulation. These are based on r2 +(rKπ)2+2r rKπcos(δ +δKπ+γ), (5) B D B D B D efficiencies,resolutionsandbackgroundlevelsob- wherethe constantofproportionalityisthe same tained from the full simulation. in each expression. The relative rates of the four Inourstudiesweuse thefollowinginformation processes yield three observables which depend to discriminate between signal and background on five parameters γ, r , rKπ, δ and δKπ, of events: charged particle identification informa- B D B D which rKπ is already well known. It is necessary tionbasedontheRingImagingCherenkovdetec- D to use different D decays in order to determine tors; invariantmasses; impact parameters;trans- verse momenta; χ2 of decay vertices of the B, D, all parameters. K∗ and K0 particles; the opening angle between Similarly, the four-body decay D0 → Kπππ S provides three new observables which depend on the momentum direction of a B and its flight di- γ, r , δ and two new parameters rK3π and rection; the event topology itself. B B D δK3π 2. Further information can be added by All selection cuts are optimized to reject most D including D decays to CP-eigenstates, such as background events from a large sample of inclu- sive b¯b events while retaining a reasonable sig- K+K− and π+π−. Each provides one more ob- servable without introducing any new parame- nal efficiency. The ratio of background to signal, B/S,isassessedusingaseparateinclusiveb¯bsam- ters: ple. Γ(B− →(h+h−) K−)∝1+(r )2+2r cos(δ −γ),(6) D B B B 3. ADS METHOD AND SENSITIVITY Γ(B+ →(h+h−)DK+)∝1+(rB)2+2rBcos(δB+γ).(7) 3.1. Description of the method 2 In fact the inclusion of D0 → Kπππ will bring many moreparameters–andadditionalinformation–becauseof Atwood,DunietzandSoni(ADS)[7]suggested theresonantsubstructureofthedecay. Thiscomplication a method of determining γ based on the recon- isneglected inthepresentdiscussion. 3 3.2. Performance with charged B mesons of data and the background-to-signal ratio B/S Results from the B factories favour a small aregiveninTab.3. Thecorrespondingstatistical value of r for charged B decays [8,9]. We set precisionoftheangleγ isexpectedtobe7o−10o. B r =0.077for this study. The followingassump- B tions are made: rKπ = rK3π = 0.06, −25o < 4. DALITZ METHOD AND SENSITIV- D D δKπ <25o and −180o<δK3π <180o. ITY D D Tab. 1 shows the expected signal and back- ground yields in 2 fb−1 of data. Of the 17.7 k 4.1. Three-body D decay This method for determining γ was proposed backgroundeventsinthefavouredB →(Kπ) K D in [10]. It makes use of the decay B± → DK± modes, 17.0 k are from the decay B → Dπ, followed by a multibody D decay into a CP whichhasa 13times largerbranchingratio,with eigenstate Here we explain the basic idea us- a π misidentified as a K, and 0.7 k are combi- ing D → K0π+π− as an example. The Dalitz natorial background events. In the suppressed S phase space of this decay D → K0π+π− can B → (Kπ) K modes, the combinatorial back- S D be fully parameterized with two effective masses ground dominates. m2 ≡ m2(K0π+) and m2 ≡ m2(K0π−). The Our simulation study indicates that the signal + S − S D0 and D¯0 decay amplitudes can be written as yields and background level are very similar for functions f(m2,m2) and f(m2,m2). theD →K3π modes. Thereforeweusethe same − + + − The total Dalitz decay amplitudes, defined as yields and B/S as in D →Kπ. A− ≡ A(B− → (K0π+π−) K−) and A+ ≡ A large number of fast samples are generated S D A(B+ → (K0π+π−) K+), are sums of contri- based on the yields and background levels given S D butions via D0 and D¯0: above to estimate the statistical precision of γ. As shown in Tab. 2 a precision of 5o − 15o for A− =f(m2,m2)+r ei(−γ+δB)f(m2,m2), (8) γ is achievable for 2 fb−1 of data, depending on − + B + − the parameter values of δKπ and δK3π and with D D A+ =f(m2,m2)+r ei(γ+δB)f(m2,m2). (9) r = 0.077. Better precision can be achieved for + − B − + B larger rB values. In the isobarmodel [11]f(m2,m2) is a coher- + − LHCbis alsoinvestigatingthe feasibility to in- ent sum of contributions of different resonances: cludethedecayB± →D∗0K± intheADSanaly- sis. AnattractivefeatureoftheD∗0mesonisthat N it can decay to two final states D0π0 and D0γ. f(m2+,m2−)=XajeiαjAj(m2+,m2−)+beiβ, (10) These have opposite CP eigenvalues, which lead j=1 toadifferenceofπ intheirstrongphases. Thisis wherea ,α ,bandβ aremodelparameterswhich j j a useful constraint if the two decays can be dis- have been measured well at the B factories [2,3]. tinguishedexperimentally. However,thesedecays The B± decay rates are given by aredifficult tofully reconstructinLHCbbecause the detection efficiency of a soft photon in the electromagnetic calorimeter is very low while the Γ−(m2,m2)=|f(m2,m2)|2+r2|f(m2,m2)|2 + − − + B + − backgroundis enormous. Alternative approaches which employ a partial reconstruction or which +2r Re[f∗(m2,m2)f(m2,m2)ei(−γ+δB)],(11) B − + + − makeuseoftheeventtopologytoreconstructthe momentum of the π0/γ are under study. Γ+(m2+,m2−)=|f(m2+,m2−)|2+rB2|f(m2−,m2+)|2 +2r Re[f∗(m2,m2)f(m2,m2)ei(γ+δB)]. (12) 3.3. Performance with neutral B mesons B + − − + The same method can also be applied to the We canseethatthe interferencetermsaresen- decay B¯0 → DK¯∗0 with D → Kπ, KK or ππ. sitivetoγ,whichcanbedeterminedbymeasuring Assuming r =0.4, 55o < γ <105o and −20o < Γ−(m2,m2) and Γ+(m2,m2) across the Dalitz B + − + − δ < 20o, the expected signal yields in 2 fb−1 phase space. B 4 Table 1 Expected signal yields S, number of background events B and the rato B/S in 2 fb−1 of data for ADS decay modes of B± corresponding to δ = 130o and δKπ = 0o. The uncertainty on the background B D estimates is around 60% for the rarest modes. decay mode S B B/S B+ →(K+π−) K+ 28 k 17.7 k 0.6 D B− →(K−π+) K− 28 k 17.7 k 0.6 D B+ →(K−π+) K+ 530 770 1.5 D B− →(K+π−) K− 180 770 4.3 D B+ →(K+K−/π+π−) K+ 4.3 k 4.3 k 1.0 D B− →(K+K−/π+π−) K− 3.3 k 3.3 k 1.0 D Table 2 The statistical error of γ for different values of δKπ and δK3π for r =0.077. Numbers with ∗ are RMS D D B values quoted for non-Gaussian distribution of fit results due to close lying ambiguous solutions. These will disappear as the signal yields increase. δKπ −25o −16.6o −8.3o 0o 8.3o 16.6o 25o D δK3π =−180o 8.6o 7.5o 6.5o 6.8o∗ 7.2o∗ 7.3o∗ 6.0o∗ D δK3π =−120o 6.0o 6.3o 6.3o 6.4o 6.2o 6.2o 4.7o D δK3π =−60o 8.0o 7.9o 8.1o 7.8o 7.4o 6.7o 6.2o D δK3π =0o 10.3o∗ 11.1o∗ 12.o∗ 11.5o∗ 12.1o∗ 13.1o∗ 13.0o∗ D δK3π =60o 9.1o 10.6o 11.2o 12.9o 13.4o∗ 15.0o∗ 15.2o∗ D δK3π =120o 11.6o∗ 11.3o∗ 11.8o∗ 11.0o∗ 10.9o∗ 11.1o 10.9o D δK3π =180o 8.5o 7.4o 6.5o 6.8o 7.1o 7.3o 6.5o D To reconstruct the B± → (K0π+π−) K± σ ≈8o−16o isachievablein2fb−1 ofdata. The S D γ events is challenging with the LHCb detector as actual statistical precision will depend on the fi- only 25% of the K0 particles decay inside the nal backgroundlevel and on r . S B active region of the vertex detector. The ex- LHCb is also investigating the decays B± → pected signal yield in 2 fb−1 of data will vary (K0K+K−) K± and B0 →(K0π+π−) K∗0. S D S D between 1.5 k and 5 k, depending on how many of the K0 decays successfully found offline can 4.2. Four-body D decay S be reconstructed within the CPU constraints of TheDalitzmethodcanbeextendedfromthree the High Level Trigger. A full simulation has to four-body D decays. In this case five param- beenperformedtoestimatethebackgroundlevel. eters are required to describe the Dalitz phase Thecombinatorialbackgroundisexpectedtocon- space. The D decay model has been studied in tribute less than 3.5 k events and contamina- the FOCUSexperiment[12]andourγ sensitivity tion from B± → (KS0π+π−)Dπ± is expected to studies are based on their results. be around 1200 events. Our present sensitivity Assuming a branching ratio of B(B± → studies for γ do not include background, and do (K+K−π+π−) K±)=9.5×10−7,ourfullsimu- D not take into account the non-flat acceptance ef- lationyields1.7k eventsin2fb−1 ofdata. 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